Here we are going to discuss, what are the factors of 43 and how many factors 43 has and what are the factors of 43 in pairs. Here are some methods, showing how to find the factors of 43.
Actually, Factor is a number which divides any number completely without leaving remainder.
Or simply we can say that if we multiply two whole numbers (positive & negative) and it gives a product. Then the numbers that we multiply, are the factors of the product.
For example, if we multiply 3 to 5, it gives 15. Here 3 and 5 are positive factors of 15 or we multiply -1 to -43, it gives 43. So -1 and -43 are negative factors of 43.
What are the factors of 43 ?
Since factors of 43 are the numbers, which divides 43 completely without leaving remainder. So here we are
going to divide 43 by all numbers up to 43. Let’s see the process –
We have to stop the process, if any number of column ‘B’ appears in column ‘A’.
Here we stop the division when 43 appears in column ‘A’, which has already been came in column ‘B’.
Actually, 43 is a Prime Number. So it divides by self only.
Hence, all factors of 43 in above table are : 1, 43
Similarly, negative factors of 43 are : -1, -43
Factor pairs of 43
As we saw in above table, 1 multiply by 43 gives 43. So (1, 943 or (43, 1) is a factor pair of 43.
Methods of Prime Factors of 43
Here we will discuss, mainly two methods of factorization to find Prime Factors of any number.
Method #1 (Division Method)
Step 1 : Divide the number by the smallest prime number, which divides the number exactly.
Step 2 : Divide the quotient again by the smallest prime number. If quotient is not exactly divisible by the
smallest prime number, choose next smallest prime number.
Step 3 : Repeat Step 2 again and again till the quotient becomes 1.
Step 4 : All the prime numbers used in above process are the prime factors.
Check : Multiply all the prime factors, the multiplication should be the number itself.
Caution : In this method, only prime numbers will be use to divide.
Take example factors of 43 and 72 to understand better.
In above example of 43,
Since 43 is a prime number, hence it will divide by itself only.
Any Prime Number has only one prime factor, i.e. itself.
Hence, 43 has only one prime factor i.e. 43.
Take another example to understand this method (Division Method).
Example of 72
Step 1 : First of all, we divide 72 by smallest prime number i.e. 2 and we got 36 as quotient and remainder is zero. (Note – if remainder will not zero, means doesn’t divide exactly, try next prime number to divide)
Step 2: Again we divide the quotient 36 by smallest prime number i.e. 2 and we got 18 as quotient.
Step 3: Repeat step 2 until we got 1 as a quotient.
Hence, 72 = 2 x 2 x 2 x 3 x 3 = 23 x 32
So 72 has two prime factor i.e. 2,& 3
Method #2 (Factor Tree Method)
Step 1 : Write a number as root of the tree
Step 2 : Find the factors of the number, each factor will be considered as root again (now, we got 2 new root)
Step 3 : Repeat step 2 until we can’t factor any more (or until we got prime factor)
Step 4 : The end nodes are the prime factors.
Factor Tree of 43
We can initiate the tree by choosing any two factors. Here we choose 1 and 43 as factors of 43, and we got the
Since, 43 is a prime numbers and no more factors can be made.
Here Unique nodes are only 1 and 43. Since 1 is not a prime, so we can’t consider it is prime factor of 43. Hence Prime Factor of 43 is only 43.
Any Prime Number has same factors and prime factors.
Note:- The Factor Tree may be made so many types depends upon choosing the initial and middle factors.
Factor Tree of 72
In this example, we start making tree by choosing 4 and 18 as initial nodes. We have choice to choose any two factors as initial factors.
Further, 4 has two factors i.e. 2 and 2. And similarly 18 has two factors i.e. 2 and 9.
Similarly 9 can be split in two factors 3 and 3.
So factor tree of 72 has two unique nodes, which are 2 and 3.
Number of factors of 43
To find the number of factors, we use Method #1 (Division Method).
In our example, as we saw above 43 is a prime number and Method#1 is not applicable.
Any Prime Number has only one factors, i.e. itself.
So we can say that 43 has only one prime factors, i.e. 43.
To understand this Rule to calculate number of factors of any given number, we select our second example of 72.
72 = 23 x 32
Number of factors is = (power + 1)(power + 1)(power + 1)………. = (3 + 1)(2 + 1) = 4 x 3 = 12
and if we consider both positive and negative factors, then
total no. of factors = 12 (positive) + 12 (negative) = 24
Read Also : Factors of 9
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